What is the difference between artificial intelligence and robots?
Although there are several definitions of "robot", an essential feature of everything called "robot" is that it is capable of movement. This does not necessarily mean displacement; a robot arm in a factory also moves.

There is a single exception to this rule,  which is bot-programs like chatbots; I will discuss them later.

Artificial Intelligence does not need to move; a chess program can be argued to be an AI, but does not move. 

A robot can actually have AI; one of the definitions of robot is that it is a system, capable of autonomous movement. In order to be autonomous, to be able to make decisions of its own, a certain amount of AI may be necessary. 

There is one class of "robots" that does not move, and does not even have physical presence; bot programs, like chatbots, that operate inside systems. I do not consider them robots, because they are not physical devices operating in the real world. A chatbot can be an AI, however - a good chatbot may have some natural language processing to interact with humans in a way that humans find natural.

To summarize; an AI can exist purely in software. But to be a robot, there must be a moving physical component in the real world.